20 lines
642 B
Markdown
20 lines
642 B
Markdown
# Wyznaczyć pochodne podanych funkcji.
|
|
## 1
|
|
$y=(3-x^{4})^{2}$
|
|
$y'=2(3-x^{4})\cdot(-4x^{3})=(6-2x^{4})\cdot(-4x^{3})=-24x^{3}+8x^{7}$
|
|
## 2
|
|
$y=1-\frac{4}{x^6}+\frac{3}{x^7}$
|
|
$y'=-4\cdot-6x^{-7}+3\cdot-7x^{-8}=\frac{24}{x^{7}}-\frac{21}{x^{8}}$
|
|
## 3
|
|
$y=\cfrac{x^{2}+4}{x}$
|
|
$y'=\cfrac{1}{x^{2}}\cdot\left(2x^{2}-(x^{2}+4)\right)=\cfrac{x^{2}-4}{x^{2}}=1-\cfrac{4}{x^2}$
|
|
## 4
|
|
$y=\cfrac{x-3}{x^{2}}$
|
|
$y'=\cfrac{1}{x^{4}}\cdot\left(x^{2}-2x^{2}+6x\right)=\cfrac{6x-x^{2}}{x^{4}}=\cfrac{6-x}{x^3}$
|
|
## 5
|
|
$y$
|
|
## 7
|
|
$y=\cfrac{x^{5}+x^{3}+x}{\sqrt{x}}$
|
|
$y'=\cfrac{1}{x}\left((x^{5}+x^{3}+x)\cdot\frac{1}{2\sqrt{x}}-(5x^{4}+3x^2+1)\cdot\sqrt{x}\right)$
|
|
|